It is proposed
that this filing will become effective (check appropriate box)

¨

immediately upon filing pursuant to paragraph (b)

x

on October 30, 2013 pursuant to paragraph (b)

¨

60 days after filing pursuant to paragraph (a)(1)

¨

on (date) pursuant to paragraph (a)(1)

¨

75 days after filing pursuant to paragraph (a)(2)

¨

on (date) pursuant to paragraph (a)(2) of Rule 485.

If appropriate, check the following box:

¨

this post-effective amendment designates a new effective date for a previously filed post-effective amendment.

ROBERT T.
BURNS, Vice President

PUTNAM FUNDS TRUST

One Post Office Square

Boston, Massachusetts 02109

(Name and address of agent for service)

Copy to:

JOHN W. GERSTMAYR, Esquire

ROPES & GRAY LLP

Prudential Tower

800
Boylston Street

Boston, MA 02199-3600

This Post-Effective Amendment
relates solely to the Registrants Putnam International Value Fund and Putnam Small Cap Growth Fund series. Information contained in the Registrants Registration Statement relating to any other series of the Registrant is neither amended
nor superseded hereby.

SIGNATURES

Pursuant to the requirements of the Securities Act of 1933 and the Investment Company Act of 1940, the Registrant certifies that it meets all of the
requirements for effectiveness of this Registration Statement under Rule 485(b) under the Securities Act of 1933 and has duly caused this Amendment to its Registration Statement to be signed on its behalf by the undersigned, duly authorized, in the
City of Boston, and The Commonwealth of Massachusetts, on the 15th day of November, 2013.

Putnam Funds Trust

By: /s/ Jonathan S. Horwitz,

Executive Vice President,

Principal Executive
Officer and Compliance Liaison

Pursuant to the requirements of the Securities Act of 1933, this Amendment to the Registration Statement
of Putnam Funds Trust has been signed below by the following persons in the capacities and on the dates indicated: